My understanding, though I may be wrong, is that you can apply for nz super under the reciprocal rights legislation. This entitles you to NZ super bowl t your U.K. Pension is paid to the NZ government. If it is a basic state pension the NZ pension is normally slightly higher - at least at current exchange rates. Issues arise if there is a serps or state second pension element as this is included also paid to NZ govt.
My understanding is that if there is a high proportion of 2nd pension you are often better off getting your UK pension direct.note there is a s not increase in this once you leave the U.K.and you are subject to FX variations. Occupational pensions are paid direct and subject to FX in the beneficiary's hands. For 4 years on arrival these are not subject to NZ tax .- normal new migrant tax rules.
Advice is definitely needed in this area as it is quite complex.